Probabilistic cross-identification of astronomical sources

We present a general probabilistic formalism for cross-identifying astronomical point sources in multiple observations. Our Bayesian approach, symmetric in all observations, is the foundation of a unified framework for object matching, where not only spatial information, but also physical properties, such as colors, redshift, and luminosity, can be considered in a natural way. We provide a practical recipe to implement an efficient recursive algorithm to evaluate the Bayes factor over a set of catalogs with known circular errors in positions. This new methodology is crucial for studies leveraging the synergy of today's multiwavelength observations and to enter the time domain science of the upcoming survey telescopes.